Logarithmic Correlation Functions in Two Dimensional Turbulence

We consider the correlation functions of two-dimensional turbulence in the presence and absence of a three-dimensional perturbation, by means of conformal field theory. In the persence of three dimensional perturbation, we show that in the strong coupling limit of a small scale random force, there is some logarithmic factor in the correlation functions of velocity stream functions. We show that the logarithmic conformal field theory c8,1 describes the 2Dturbulence both in the absence and in the presence of the perturbation. We obtain the following energy spectrum E(k) ∼ k−5.125 ln(k) for perturbed 2D turbulence and E(k) ∼ k−5 ln(k) for unperturbed turbulence. Recent numerical simulation and experimental results confirm our prediction.